Arithmetic in large ring and field extensions is an important problem of symbolic computation, and it consists essentially of the combination of one multiplication and one division in the underlying ring. Methods are known for replacing one division by two short multiplications in the underlying ring, which can be performed essentially by using convolutions. However, while using school-book mul...

We give an explicit criterion for the irreducibility of some induction products of evaluation modules of affine Hecke algebras of type A. This allows to describe the form of the zeros and poles of the trigonometric R-matrix associated to any evaluation module of Uv(ŝlN ). Abridged english version — Let Ĥn(u) be the affine Hecke algebra associated to GL(n) and Hn(u) its finite-dimensional subalg...

Module skew codes are one sidedmodules for (a quotient of) a skewpolynomial ringwhere multiplication is twisted by an automorphism of the Galois group of the alphabet field. We prove that long module skew codes over a fixed finite field are asymptotically good by using a non-constructive counting argument. We show that for fixed alphabet size, and automorphism order and large length their asymp...

On path space kQ, there is a trivial kQ-module structure determined by the multiplication of path algebra kQ and a trivial kQ-comodule structure determined by the comultiplication of path coalgebra kQ. In this paper, on path space kQ, a nontrivial kQ-module structure is defined, and it is proved that this nontrivial left kQ-module structure is isomorphic to the dual module structure of trivial ...

We generalize various properties of Yetter-Drinfeld modules over Hopf algebras to quasi-Hopf algebras. The dual of a finite dimensional Yetter-Drinfeld module is again a Yetter-Drinfeld module. The algebra H 0 in the category of Yetter-Drinfeld modules that can be obtained by modifying the multiplication in a proper way is quantum commutative. We give a Structure Theorem for Hopf modules in the...

Let R be a G-graded ring and M be a G-graded R-module. In this article, we introduce the concept of graded weakly classical prime submodules and give some properties of such submodules.

We present a novel randomized algorithm to factor polynomials over a finite field Fq of odd characteristic using rank 2 Drinfeld modules with complex multiplication. The main idea is to compute a lift of the Hasse invariant (modulo the polynomial f ∈ Fq[x] to be factored) with respect to a random Drinfeld module φ with complex multiplication. Factors of f supported on prime ideals with supersin...

The paper presents the concepts behind the "Urdhva Tiryagbhyam Sutra" and "Nikhilam Sutra" multiplication techniques. It then shows the architecture for a 16×16 Vedic multiplier module using Urdhva Tiryagbhyam Sutra. The paper then extends multiplication to 16×16 Vedic multiplier using "Nikhilam Sutra" technique. The 16×16 Vedic multiplier module using Urdhva Tiryagbhyam Sutra uses four 8×8 Ved...

The thermal safety of lithium-ion traction batteries is a highly concerning issue in the field electric transportation. large amount gas emissions during runaway process has high hazards, such as fire and explosion. quantitative analysis one important challenges testing evaluating battery safety. Focusing on quantifying using large-scale propagation modules packs, based idea cell result multipl...

Bit-sequential multiplier is being studied in a (+1, -1) binary representation. The maximum length of multiplier for a fix point numbers consists of n module. Each module is a five bit adder which contains 5 inputs and 3 outputs. It also contains an additional pin at the input as well as at the output. Computation time for multiplication is of the order of O(n). Hardware realization of module i...